Deck 53: Arithmetic Sequences and Partial Sums

Question 1

Determine whether the sequence is arithmetic.If so,find the common difference. ​
​ln4,ln5,ln6,ln7,ln8,...
​

A)Arithmetic sequence,d = 0.41
B)Arithmetic sequence,d = -0.22
C)Arithmetic sequence,d = -0.56
D)Arithmetic sequence,d = 0.22
E)Not an arithmetic sequence

Answer 1

Not an arithmetic sequence

Question 2

Determine whether the sequence is arithmetic.If so,find the common difference. ​
​128,64,32,16,8,...
​

A)Arithmetic sequence,d = -120
B)Arithmetic sequence,d = -8
C)Arithmetic sequence,d = 8
D)Arithmetic sequence,d = 24
E)Not an arithmetic sequence

Answer 2

Not an arithmetic sequence

Question 3

Determine whether the sequence is arithmetic.If so,find the common difference. ​
3²,4²,5²,6²,7²,...
​

A)Arithmetic sequence,d = -33
B)Arithmetic sequence,d = 16
C)Arithmetic sequence,d = -27
D)Arithmetic sequence,d = 7
E)Not an arithmetic sequence

Answer 3

Not an arithmetic sequence

Question 4

Find a formula for a_n for the arithmetic sequence. ​
A₁ = 4,d = 7
​

A)a_n ​= -7n + 11
B)a_n ​= 7n - 3
C)a_n ​= 7n + 3
D)a_n ​= -7n ​+ 3
E)a_n ​= 7n - 11

Question 5

Determine whether the sequence is arithmetic.If so,find the common difference. ​
​16,14,12,10,8,...
​

A)Arithmetic sequence,d = -8
B)Arithmetic sequence,d = 2
C)Arithmetic sequence,d = ​4
D)Arithmetic sequence,d = -2
E)Not an arithmetic sequence

Question 6

Find a formula for a_n ​for the arithmetic sequence. ​
A₁ = 104,d = -6
​

A)a_n ​= -6n + 98
B)a_n ​= 6n + 110
C)a_n ​= 6n - 98
D)a_n ​= 6n - 110
E)a_n ​= -6n + 110

Question 7

Determine whether the sequence is arithmetic.If so,find the common difference. ​
​4)8,5.4,6,6.6,7.2,...
​

A)Arithmetic sequence,d = -0.6
B)Arithmetic sequence,d = 7.2
C)Arithmetic sequence,d = 1.2
D)Arithmetic sequence,d = 0.6
E)Not an arithmetic sequence

Question 8

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so,find the common difference.(Assume that n begins with 1. ) ​
A_n = 6 + 4n
​

A)38,34,30,26,22 Arithmetic sequence
D = -4
B)22,26,30,34,38 Arithmetic sequence
D = 4
C)10,14,18,22,26 Arithmetic sequence
D = -4
D)26,22,18,14,10 Arithmetic sequence
D = -4
E)10,14,18,22,26 Arithmetic sequence
D = 4

Question 9

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so,find the common difference.(Assume that n begins with 1. ) ​
A_n = 5 - 6(n - 4)
​

A)-13,-7,-1,5,11 Arithmetic sequence
D = -6
B)-1,5,11,17,23 Arithmetic sequence
D = -6
C)23,17,11,5,-1 Arithmetic sequence
D = 6
D)11,5,-1,-7,-13 Arithmetic sequence
D = 6
E)23,17,11,5,-1 Arithmetic sequence
D = -6

Question 10

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so,find the common difference.(Assume that n begins with 1. ) ​
A_n = 4n - ¹
​

A)1,4,16,64,256 Arithmetic sequence
D = -4
B)256,64,16,4,1 Not an Arithmetic sequence
C)1,4,16,64,256 Not an Arithmetic sequence
D)256,64,16,4,1 Arithmetic sequence
D = 4
E)1,4,16,64,256 Arithmetic sequence
D = 4

Question 11

Determine whether the sequence is arithmetic.If so,find the common difference. ​
​2,4,8,16,32,...
​

A)Arithmetic sequence,d = 6
B)Arithmetic sequence,d = 2
C)Arithmetic sequence,d = -2
D)Arithmetic sequence,d = -30
E)Not an arithmetic sequence

Question 12

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so,find the common difference.(Assume that n begins with 1. ) ​
A_n = 2 + (n ​- 2)5
​

A)17,12,7,2,-3 Arithmetic sequence
D = -5
B)-3,2,7,12,17 Arithmetic sequence
D = 5
C)-3,2,7,12,17 Arithmetic sequence
D = -5
D)32,27,22,17,12 Arithmetic sequence
D = -5
E)12,17,22,27,32 Arithmetic sequence
D = 5

Question 13

Find a formula for a_n ​for the arithmetic sequence. ​
A₁ = 16,d = 6
​

A)a_n ​= -6n​ + 22
B)a_n ​= -6n + 10
C)a_n ​= 6n ​- 10
D)a_n ​= 6n + 10
E)a_n ​= 6n - 22

Question 14

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so,find the common difference.(Assume that n begins with 1. ) ​
A_n = 135 - 5n
​

A)110,115,120,125,130 Arithmetic sequence
D = -5
B)105,110,115,120,125 Arithmetic sequence
D = 5
C)130,125,120,115,110 Arithmetic sequence
D = 5
D)130,125,120,115,110 Arithmetic sequence
D = -5
E)125,120,115,110,105 Arithmetic sequence
D = 5

Question 15

Determine whether the sequence is arithmetic.If so,find the common difference. ​
7,12,17,22,27,...
​

A)Arithmetic sequence,d = 5
B)Arithmetic sequence,d = 10
C)Arithmetic sequence,d = -5
D)Arithmetic sequence,d = -27
E)Not an arithmetic sequence

Question 16

Determine whether the sequence is arithmetic.If so,find the common difference. ?
7, $\frac { 13 } { 2 }$ ,6, $\frac { 11 } { 2 }$ ,5,...
?

A)Arithmetic sequence,d = -1
B)Arithmetic sequence, $d = \frac { 3 } { 2 }$
C)Arithmetic sequence, $d = - \frac { 1 } { 2 }$
D)Arithmetic sequence,d = -2
E)Not an arithmetic sequence

Question 17

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so,find the common difference.(Assume that n begins with 1. ) ​
A_n = (-2)n
​

A)​-2,4,-8,16,-32 Not an Arithmetic sequence
B)-32,-16,-8,-4,-2 Arithmetic sequence
D = 2
C)-2,4,-8,16,-32 Arithmetic sequence
D = -2
D)-2,4,-8,-16,-32 Arithmetic sequence
D = 2
E)-32,-16,-8,4,-2 Not an Arithmetic sequence

Question 18

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so,find the common difference.(Assume that n begins with 1. ) ​
A_n = (2n)n
​

A)2,8,24,64,160 Arithmetic sequence
D = -2
B)160,64,24,8,2 Arithmetic sequence
D = 2
C)160,64,24,8,2 Not an Arithmetic sequence
D)2,8,24,64,160 Arithmetic sequence
D = 2
E)2,8,24,64,160 Not an Arithmetic sequence

Question 19

Determine whether the sequence is arithmetic.If so,find the common difference. ​
​5)3,5.7,6.1,6.5,6.9,...
​

A)Arithmetic sequence,d = -0.4
B)Arithmetic sequence,d = -1.6
C)Arithmetic sequence,d = 0.8
D)Arithmetic sequence,d = 0.4
E)Not an arithmetic sequence

Question 20

Determine whether the sequence is arithmetic.If so,find the common difference. ?
3, $\frac { 11 } { 4 }$ , $\frac { 5 } { 2 }$ , $\frac { 9 } { 4 }$ ,2,...
?

A)Arithmetic sequence, $d = - \frac { 1 } { 4 }$
B)Arithmetic sequence,d = $\frac { 1 } { 4 }$
C)Arithmetic sequence,d = -1
D)Arithmetic sequence, $d = \frac { 3 } { 4 }$
E)Not an arithmetic sequence

Question 21

Find a formula for a_n ?for the arithmetic sequence. ?a₃ = 94,a₆ = 87
?

A)a_n ?= $\frac { 7 } { 3 }$ n - 101
B)a_n ?= $- \frac { 7 } { 3 }$ n + 101
C)a_n ?= 101 - 303n
D)a_n ?= $\frac { 7 } { 3 }$ n + 303
E)a_n ?= 101 + 303n

Question 22

Determine whether the sequence is arithmetic.If so,find the common difference. 2,7,12,17,22

A)-5
B)-3
C)5
D)not arithmetic
E)2

Question 23

Write the first five terms of the arithmetic sequence. ​
A₁ = 4,a₁₂ = 48
​

A)-4,-12,-20,-22,-24
B)-4,-8,-12,-16,-20
C)20,16,12,8,4
D)-4,-12,-20,-8,-16
E)4,8,12,16,20

Question 24

Determine whether the sequence is arithmetic.If so,find the common difference.(Assume that n begins with 1. ) ​
A_n ​= 8 + 6n
​

A)-6
B)-8
C)6
D)8
E)not arithmetic

Question 25

Write the first five terms of the arithmetic sequence defined recursively. ​
A₁ = 0.275,an _{+ 1} = a_n + 0.25
​
​

A)0.275,0.525,0.775,1.025,1.775
B)-0.275,-0.525,-0.775,-1.025,-1.275
C)0.275,0.525,0.775,1.025,1.525
D)-0.275,-0.525,-0.775,-1.025,-1.525
E)0.275,0.525,0.775,1.025,1.275

Question 26

Write the first five terms of the arithmetic sequence. ​
A₁ = -3.6,d = -0.6
​

A)4.2,4.8,5.4,6,6.6
B)-3.6,-4.2,-4.8,-5.4,-6
C)3.6,4.2,4.8,5.4,6
D)-4.2,-4.8,-5.4,-6,-6.6
E)3.6,4.2,4.8,5.4,6.6

Question 27

The first two terms of the arithmetic sequence are given.Find the missing term. ​
A₁ = 7,a₂ = 11,a₁₀ = ?
​

A)39
B)31
C)43
D)47
E)35

Question 28

Write the first five terms of the arithmetic sequence defined recursively. ​
A₁ = 206,an _{+ 1} = a_n - 14
​
​

A)-206,-192,-178,-164,-136
B)206,192,178,164,122
C)206,192,178,164,150
D)-206,-192,-178,-164,-150
E)206,192,178,164,136

Question 29

Write the first five terms of the arithmetic sequence. ​
A₁ = 8,d = 8
​

A)16,24,32,40,8
B)8,16,24,32,48
C)8,16,24,32,40
D)16,24,32,40,48
E)8,0,24,32,40

Question 30

Write the first five terms of the arithmetic sequence defined recursively.? $$a _ { 1 } = \frac { 7 } { 8 } , a _ { n + 1 } = a _ { n } - \frac { 5 } { 8 }$$ ? ?

A) $\frac { 7 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ ,-1, $- \frac { 13 } { 8 }$
B) $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ ,-1, $- \frac { 13 } { 8 }$ , $\frac { 7 } { 8 }$
C) $\frac { 7 } { 8 }$ , $- \frac { 3 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 9 } { 4 }$ ,-1
D) $\frac { 7 } { 8 }$ , $- \frac { 3 } { 8 }$ , $- \frac { 13 } { 8 }$ ,-1, $\frac { 1 } { 4 }$
E) $\frac { 7 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ ,-1, $- \frac { 9 } { 4 }$

Question 31

Find the sum of the finite arithmetic sequence. ​
3 + 7 + 11 + 15 + 19 + 23 + 27
​

A)107
B)109
C)105
D)1105
E)113

Question 32

The first two terms of the arithmetic sequence are given.Find the missing term. ​
A₁ = -0.6,a₂ = -12.8,a₈ = ?
​

A)-86
B)61.6
C)122.6
D)-98.2
E)-73.8

Question 33

Write the first five terms of the arithmetic sequence defined recursively. ​
A₁ = 17,an _{+ 1} = a_n + 4
​
​

A)17,21,25,29,33
B)-17,-21,-25,-29,-33
C)17,21,25,29,41
D)-17,-21,-25,-29,-37
E)17,21,25,29,37

Question 34

Find a formula for a_n ?for the arithmetic sequence. ?
A₁ = 8,a₄ = 18
?

A)a_n ?= $\frac { 14 } { 3 }$ + 14n
B)a_n ?= $\frac { 14 } { 3 }$ - 14n
C)a_n ?= $\frac { 10 } { 3 }$ n - $\frac { 14 } { 3 }$
D)a_n ?= $\frac { 10 } { 3 }$ n + 14
E)a_n ?= $\frac { 10 } { 3 }$ n + $\frac { 14 } { 3 }$

Question 35

Find a formula for a_n ?for the arithmetic sequence. ?
A₁ = 0,d = - $\frac { 6 } { 7 }$ ?

A)a_n ?= $\frac { 6 } { 7 }$ n - $\frac { 6 } { 7 }$
B)a_n ?= - $\frac { 7 } { 6 }$ n - $\frac { 7 } { 6 }$
C)a_n ?= - $\frac { 6 } { 7 }$ n + $\frac { 6 } { 7 }$
D)a_n ?= $\frac { 6 } { 7 }$ n + $\frac { 6 } { 7 }$
E)a_n ?= - $\frac { 7 } { 6 }$ n + $\frac { 7 } { 6 }$

Question 36

Determine whether the sequence is arithmetic.If so,find the common difference. 5,25,125,625,3125

A)-5
B)5
C)5n - 5n ^{- 1}
D)not arithmetic
E)​5n

Question 37

The first two terms of the arithmetic sequence are given.Find the missing term. ​
A₁ = 2.2,a₂ = 3.6,a₇ = ?
​

A)13.4
B)12
C)16.2
D)9.2
E)10.6

Question 38

Find a formula for a_n ​for the arithmetic sequence. ​
16,11,6,1,-4,...
​

A)a_n ​= 1 - 5n
B)a_n ​= 1 + 5n
C)a_n ​= -5n + ​21
D)a_n ​= 5n - 21
E)a_n ​= 5n + 21

Question 39

Find the sum of the finite arithmetic sequence. ​
​2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20
​

A)90
B)80
C)70
D)100
E)110

Question 40

Find a formula for a_n ?for the arithmetic sequence. ?
A₁ = -5,a₅ = 18
?

A)a_n ?= $\frac { 23 } { 4 }$ n - $\frac { 43 } { 4 }$
B)a_n ?= $\frac { 23 } { 4 }$ n + 43
C)a_n ?= $\frac { 43 } { 4 }$ - 43n
D)a_n ?= $\frac { 43 } { 4 }$ + 43n
E)a_n ?= $\frac { 23 } { 4 }$ n + $\frac { 43 } { 4 }$

Question 41

Write the nth term of the arithmetic sequence as a function of n. ​
A₁ = -7,ak _{+ 1} = a_k + 4

A)an = 3 + 4n
B)an = -7 + 4n
C)an = 11 - 7n
D)an = -3 + 4n
E)an = -11 + 4n

Question 42

Find the indicated nth partial sum of the arithmetic sequence. 1.5,3.1,4.7,6.3,.... ,n = 40

A)1,234
B)1,308.1
C)1,308
D)1,307.9
E)1,372

Question 43

Find a formula for a_n for the arithmetic sequence. ?
A₁ = 7,d = -8
?

A) $a _ { n } = 7 \left( - \frac { 1 } { 8 } \right) ^ { n - 1 }$
B) $a _ { n } = - 8 + 7 ( n - 1 )$
C) $a _ { n } = 7 - 9 n$
D)? $$a _ { n } = 15 - 8 n$$
E) $a _ { n } = 7 - 8 ^ { n - 1 }$

Question 44

Several logs are stored in a pile with 30 logs on the bottom layer,29 on the second layer,28 on the third layer,and so on.If the top layer has one log,how many logs are in the pile? ​

A)464
B)465
C)450
D)435
E)none of the above

Question 45

Write the first six terms of the arithmetic sequence with the given properties. ​
A​₁ = 3,d = 4
​

A)4,8,12,16,20,24
B)3,7,11,15,19,23
C)3,6,9,12,15,18
D)4,7,10,13,16,19
E)3,8,12,16,20,24

Question 46

Use a graphing utility to graph the first 10 terms of the sequence.(Assume that n begins with 1. )You may need to adjust the graphing window to the sizes indicated below to answer the question. ​
​a_n = -0.4n + 12
​

A) ​
B)
C)​
D)
E)

Question 47

Match the arithmetic sequence with its graph from the choices below. ​
​a_n = 35 - 3n
​

A)​
B) ​
C)
D) ​
​
E)

Question 48

Write the first five terms of the arithmetic sequence. ​
A₁ = 5,d = 7
​

A)5,12,19,26,33
B)12,19,26,33,40
C)5,-2,-9,-16,-23
D)5,12,17,22,27
E)5,35,245,1715,12005

Question 49

Write the first five terms of the arithmetic sequence.? $a _ { 5 } = 1 , a _ { 15 } = 21$ ?

A)-5,-3,-1,1,3
B)-7,-14,-28,-56,-112
C)-7,-9,-11,-13,-15
D)-7,-5,-12,-19,-26
E)-7,-5,-3,-1,1

Question 50

The first two terms of the arithmetic sequence are given.Find the indicated term.? $a _ { 1 } = - 1 , a _ { 2 } = 6 , a _ { 11 } =\square$ ?

A)-3
B)69
C)76
D)83
E)-4

Question 51

Find the partial sum.? $\sum _ { n = 1 } ^ { 240 } - 3 n - 1$ ?

A)-87,724
B)-86,520
C)-86,279
D)-87,000
E)-87,001

Question 52

Find a formula for a_n for the arithmetic sequence.? $$a _ { 3 } = 0 , a _ { 9 } = - 12$$ ?

A)a_n ?= 4 - 2n
B)a_n ?= -6 + 4n?
C)a_n ?= - 2 + 4n?
D)a_n ?= 6 - 2n?
E)a_n ?= 4n